1. Commutative law
Associative law

2. Let’s play a game. （1）70、50、30 （2）32、40、68 （3）100、150、850
Find the sum of three numbers in least time.
（1）70、50、30
（2）32、40、68
（3）100、150、850
Add up to the tens 、hundreds or thousands

3. Task 1
The dates below are school open days where the whole class sells fruit juice to raise money for charity.
Sales
Date
Nov. 1st
Nov. 2nd
Nov. 3rd
Apple juice（tin） 63 55 45
Q:How many tins of fruit juice were sold on these dates in total?

4. Task 1
63＋55＋45
=（63＋55）＋45
= 118＋45
= 163
63＋55＋45
=63＋（55＋45）
=63＋100
=163
What is the same and what is different between the two number sentences?
（63＋55）＋45=63＋（55＋45）

5. Task 1 （27+36）+64=27+（36＋64） 27＋36＋64 27＋36＋64 =27＋（36＋64） =27＋100
=127
=（27＋36）＋64
= 63＋64
= 127
（27+36）+64=27+（36＋64）

6. Who can create a similar question?
Task 1
（63＋55）＋45=63＋（55＋45）
（27+36）+64=27+（36＋64）
Who can create a similar question?

7. Their sum remains the same.
Task 1
To add three numbers
Add the first two numbers
Now add the third number. Or
Add the last two numbers
Now add the first number.
Their sum remains the same.
associative law of addition

8. Algebraic expression:
Task 1
Algebraic expression:
(a + b) + c = a + (b + c)

9. Follow-up exercises （33＋16）＋84= ＋（16＋ ） （168＋24）＋76= ＋（ ＋ ）
Fill in the blanks by using the associative law of addition
（33＋16）＋84= ＋（16＋ ）
（168＋24）＋76= ＋（ ＋ ）
（25＋ ）＋72= ＋（28＋72）
（a＋ ）＋c=a＋（b＋ ） 33 84 24 76
168 28 25 c b

10. Task 2
Danny's father bought 3 boxes of juice. There are 25 cans per box and each can costs £4.
How much did his father pay in total?
3×25 ×4

11. Task 2 3×25×4 3×25×4 =（3×25）×4 =3×（25×4） = 75×4 =3×100 = 300 =300
= 75×4
= 300
3×25×4
=3×（25×4）
=3×100
=300
Which method is better?
（3×25）×4= 3×（25×4）

12. Task 2 26×8×125 =26×（8×125） 26×8×125 =（26×8）×125 = 208×125 =26×1000
26×8× =26×（8×125）
26×8×125
=（26×8）×125
= 208×125 =
=26×1000
=26000
（26×8）×125= 26×（8×125）
（□×□）×□= □×（□×□）

13. Who can create a similar question?
Task 2
（3×25）×4= 3×（25×4）
（26×8）×125= 26×（8×125）
Who can create a similar question?

14. To multiply three numbers
Task 2
To multiply three numbers
Multiply the first two numbers
Now multiply by the third number. Or
Multiply the last two numbers
Now multiply by the first number.
Their product remains the same.
associative law of multiplication

15. Algebraic expression:
Task 2
Algebraic expression:
(a × b)×c = a×(b × c)

16. Follow-up exercises 36×71×26=（ ____ × _____ ）×26
Fill in the blanks by using the associative law of addition
36×71×26=（ ____ × _____ ）×26
57×95×83=57×（ ____ × ____ ）
●×▲×★=___ ×（▲× __ ）
=（ ___ × ▲）× ____ 36 71 95 83 ● ★ ● ★

17. (a ＋ b) ＋ c = a ＋ (b ＋ c)
(a × b) × c = a × (b × c)
Compare with the associative law of addition and multiplication，what do you find?
three numbers
calculate from left to right in turn
calculate the last two numbers first
the answer remain the same

18. Exercise

19. 1、Match the number sentences
(1) a×（b×c） A. 24＋（42＋58）
(2) 76＋18＋ B. 76＋（18＋22）
(3) 24＋42＋ C. 67×（125×8）
(4)（67×125）× D. （a×b）×c

20. 2、Which number sentence conforms to the associative law?
(1) a×(b×c)=(a×b)×c  (2) 15＋(7＋3)=(15＋2)＋3
(3) (23+41)+72+28=23+41+(72+28) √ × √

21. (1) 25＋34＋66=___＋（ ___＋____ ） (2) 25×40×78=（ ____ × ____ ）×78
3、Fill in the blanks by using the associative law
(1) 25＋34＋66=___＋（ ___＋____ ）
(2) 25×40×78=（ ____ × ____ ）×78
(3) 56＋72＋44=(___＋ ___)＋72
(4) 75×8×2×125=
（ ___ × ___ ）×（ ___ × ___ ） 25 34 66 25 40 56 44 8
125 75 2

22. 4、 Solve by making the question simpler
92＋89＋11  ×5× ×17×8  
85＋41＋15＋ ×125
=92+（89+11）
=92+100
=192
=39×（5×2）
=39×10
=390
=125×8×17
=1000×17
=17000 =
=（85+15）+（41+59） =
= 200
=8×8×128
=8×（8×125）
=8×1000
=8000

23. Summary
What have you learned today？

24. John said the correct answer right away.
Using your brain:
John and Lucy are calculating
98 ＋ 998 ＋ 9998 ＋ 2 × 3,
John said the correct answer right away.
Can you？